Question: Solve for $x$ and $y$ using elimination. ${2x+2y = 20}$ ${3x-5y = 14}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $-3$ and the bottom equation by $2$ ${-6x-6y = -60}$ $6x-10y = 28$ Add the top and bottom equations together. $-16y = -32$ $\dfrac{-16y}{{-16}} = \dfrac{-32}{{-16}}$ ${y = 2}$ Now that you know ${y = 2}$ , plug it back into $\thinspace {2x+2y = 20}\thinspace$ to find $x$ ${2x + 2}{(2)}{= 20}$ $2x+4 = 20$ $2x+4{-4} = 20{-4}$ $2x = 16$ $\dfrac{2x}{{2}} = \dfrac{16}{{2}}$ ${x = 8}$ You can also plug ${y = 2}$ into $\thinspace {3x-5y = 14}\thinspace$ and get the same answer for $x$ : ${3x - 5}{(2)}{= 14}$ ${x = 8}$